Grace's Guide is the leading source of historical information on industry and manufacturing in Britain. This web publication contains 148,535 pages of information and 233,960 images on early companies, their products and the people who designed and built them.
late Kirby and Barrows
1863 June. Advert. 'Barrows and Carmichael, late Kirby and Barrows, Manufacturers of First-class Portable and Fixed Steam Engines, Threshing Machines, Steam Ploughing Apparatus etc.' 
1868 March. Advertisement as 'Barrows and Carmichael' for Threshing Machinery. 
1868 Became Barrows and Stewart
Curiously, although the partnership between Joseph Edward Kirby and Thomas Welch Barrows, trading as Kirby and Barrows, was dissolved in 1863, there is a reference to Barrows and Carmichael in 1856: 'The coming of age Mr. H. B. Samuelson, eldest son of Mr. B. Samuelson, .... congratulating the town upon the increase the Britannia works, and also the manufacturing establishment Messrs. Barrows and Carmichael, and expressing hope that there would be still more works spring up...'.